The comedy in "The Seagull" is not what we are accustomed to today. The modern terminology might be "tragicomedy"; that is, a serious play with comical moments. In the spring of 2008, The Classic Stage Company ran the play, and its director was interviewed in the New York Times. When asked about the comedy in "The Seagull," he answered:

Life is paradoxical, and Chekhov felt this paradox very acutely. Frequently what is funny turns out to be tragic, and what’s dramatic very quickly and easily becomes funny to everybody else around. I think you should look at the behavior of the characters, which I hope you will perceive as paradoxical, in order to see where the funny is in the tragic and the tragic is in the funny.

The eNotes study guide calls the play a "comedy of manners," which means that it pokes fun at the way people behave. The humor in this play, however, lies more in the sense of irony than in laughter.

I think what is comic here is, that the characters themselves drag themselves to destruction. Despite it is tragic due to the catatrophe, it remains a comedy because of the comic elements. Chekhov himself called it a comedy!